Inflation, its Volatility and the Inflation-Growth Tradeoff in India 1

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1 ASARC Working Paper 203/06 Inflaion, is Volailiy and he Inflaion-Growh Tradeoff in India Raghbendra Jha and Varsha S. Kulkarni Ausralian Naional Universiy Indiana Universiy Bloomingon USA ABSTRACT This paper amends he New Keynesian Phillips curve model o include inflaion volailiy. I provides resuls on he deerminans of inflaion volailiy and expeced inflaion volailiy for OLS and ARDL (, models and for change in inflaion volailiy and change in expeced inflaion volailiy using ECM models. Oupu gap affecs change in expeced inflaion volailiy alone (in he ECM model and no in he oher models. Major deerminans of inflaion volailiy and expeced inflaion volailiy are idenified. To he bes of our knowledge his is he firs paper o augmen he New Keynesian Phillips Curve o include inflaion volailiy. Keywords: Inflaion, Inflaion volailiy, ARDL model, ECM model, Oupu gap, India JEL classificaion: E3, E32, E42, E44 Please address all correspondence o: Prof. Raghbendra Jha, ASARC, Arnd Corden Dep of Economics, H.C. Coombs Building (09 Ausralian Naional Universiy, Canberra, ACT 0200, Ausralia Phone: , Fax: , r.jha@anu.edu.au Thoughs and views sough from Raghav Gaiha and Eric Smih were helpful for his paper. We are graeful o a summer scholarship graned o Varsha S. Kulkarni by he Sana Fe Insiue, where some of his work was compleed.

2 Raghbendra Jha & Varsha S. Kulkarni I. INTRODUCTION Recen lieraure, 2 for several counries over ime, suggess ha he volailiy of inflaion is an imporan deerminan of he radeoff beween inflaion and economic growh. I is esablished as one of he imporan facors affecing he overall volailiy for some counries and in fac a reducion in inflaion volailiy has accompanied a reducion in oupu gap volailiy. This paper explores his issue furher in he conex of a paricular counry, India. Recen analysis has indicaed he imporance of inflaion volailiy for he moneary ransmission mechanism in India (Kapur and Behera, 202. In he analysis of such moneary policy mechanisms he New Keynesian Phillips Curve (henceforh NKPC has proved o be a useful ool. Thus Para and Ray (200 for India and Brissimis and Magginas (2008 for he US find considerable suppor for he sandard NKPC. The purpose of his paper is o exend he sandard NKPC framework o include inflaion volailiy and es is significance for he case of India. The paper is organized as follows. Secions II and III describe he NKPC and he mahemaical formulaion of he incorporaion of inflaion volailiy herein, respecively. We discuss he daa and mehods of analysis in secion IV which is followed by resuls in secion V. Finally, secion VI concludes. To he bes of our knowledge his is he firs paper o exend he NKPC framework o include inflaion volailiy. II. THE NEW KEYNESIAN PHILLIPS CURVE The NKPC combines he properies of raional expecaions and sicky prices. The sicky price sipulaion follows he work of Calvo (983. A random fracion (-θ of firms is able o rese heir prices whereas he fracion θ keep heir prices unchanged. When firms change prices hey ake ino accoun he fac ha he prices may remain fixed for several periods. In line wih he lieraure i is assumed ha firms choose a log price, z, o minimize he following loss funcion: k0 k 2 L( z ( E ( z p * ( k Here >β >0 is he discoun facor and p* +k is he opimal price ha he firm would se in period +k in he absence of any price rigidiy. The erm wihin he expecaions operaor denoes he k square of he undiscouned loss. Fuure losses are discouned a he rae ( and he summaion over all possible k fuure periods shows he effec curren price on all fuure periods. If β< hen he firm would place more weigh on curren losses as compared o hose incurred in fuure. Calvo (983 derives he opimal price o be se by he firm o be: 2 For a review of his lieraure in a cross counry conex see Jha and Dang ( ASARC WP 203/06

3 Inflaion, is Volailiy and he Inflaion-Growh Tradeoff in India k k k 0 z ( ( E ( mc (2 The opimal fully flexible price in period +k is a mark-up (µ over marginal cos (mc. This implies ha he opimal loss-minimizing soluion is for he firm o se is price equal o a weighed average of he opimal fully flexible prices over ime. These weighs are declining over ime. The aggregae price level in his economy is a weighed average of las period s aggregae price level and he new rese price wih he weigh being deermined by θ. Thus: p p z (3 ( This can be re-arranged o express z as: z ( p p (4 Now, (2 is a firs order difference equaion wih he soluion given as z Ez ( ( mc (5 Subsiuing he resul in (5 ino (4 we ge (assuming ( p p ( E p p ( ( mc E p ~ p : ( ( E ( mc p (7 where p p is he rae of inflaion. Thus, inflaion depends posiively on real marginal cos ( mc p. Hence, if he raio of marginal cos o price is high firms will raise prices when reseing hese. This expression is ofen labeled he NKPC. Clearly his equaion incorporaes he effec of forward expecaions E p. Duffy and Xiao (20 show ha he neoclassical augmened Phillips Curve differs from NKPC in jus his erm. (6 III. VOLATILITY OF INFLATION We now use he sandard Phillips curve: u (8 where u is he unemploymen rae. (8 is inerpreed as a relaion beween change in inflaion and unemploymen level. ASARC WP 203/06 3

4 Raghbendra Jha & Varsha S. Kulkarni Nex we inegrae (7 and (8 and inroduce ino he resulan relaionship he noion of inflaion volailiy. Three alernaive noions of inflaion volailiy could be used: (a (b, or (c We ake he simples case (a here. So (9 Subsiuing (9 on he LHS of equaion (8 and using (7, we ge: ( ( ( mc p E = u (0 Now if u=u*, he non-acceleraing inflaion rae of unemploymen (henceforh NAIRU, we can ge a relaionship beween, E and p bu p p =0, so,so we have a relaion beween inflaion a curren ime, backward ime, forward ime. If u NAIRU, hen i can be shown ha ( incorporaes inflaion variabiliy. If mc p y hen E y E p mc ( ( ( (2 ( ( wih If we rework he NKPC using we ge: ( p z (3 as he modified form of (4. Unanicipaed inflaion is ( E which would hen be used o scale he erm E E We also know from (5 z E z ( ( mc, so from (3 above we ge E p E ( ( ( mc p Now considering, we ge (. 4 ASARC WP 203/06

5 Inflaion, is Volailiy and he Inflaion-Growh Tradeoff in India E ( ( ( E ( E p ( ( mc p From he definiion of inflaion, p p ( ( E ( E ( E p ( ( mc p If mc p y E ( E E p p ( ( y (5 ( ( Where Eq. (5 gives he relaion beween expeced fuure inflaion volailiy and he difference beween (scaled acual inflaion a previous ime and he expeced inflaion a ha ime. (4 IV. DATA & METHODS We use he yearly Consumer Price Index (henceforh CPI and Gross Domesic Produc (henceforh GDP per capia for India obained from he Inernaional Moneary Fund (henceforh IMF daabase for he period of We use he following mehods o esimae equaions (2 and (5 derived above. A. Compuing Expeced Values The oupu gap y is defined as he difference beween acual GDP per capia and he prediced or expeced GDP per capia. We compue he expeced values of GDP per capia using he model EGDP ab (6a wih an aim of fiing he ypical rend of growh rae (Dornbusch, Fischer, Sarz Here a represens he iniial GDP level and b represens he growh rae. Similarly we obain he expeced values of price (CPI, inflaion (π and volailiy of inflaion (as defined in (a above from equaions 6 b,c,d respecively as follows E p a2b2 (6b E a3b3 (6c E ( a4b4 (6d Again, he a s and b s represen he iniial level of he variable whose expeced value is calculaed and growh raes respecively. Apar from hese models he expeced values of hese variables may also be ASARC WP 203/06 5

6 Raghbendra Jha & Varsha S. Kulkarni compued using (linear model: Y or (quadraic model: Y a b c 2, a decision we make based on saisical concerns oulined below. B. Tesing for co-inegraion The Ordinary Leas Squares (OLS henceforh regressions applied above in equaions (2, (5 and (6 may be rendered spurious due o he non-saionariy of he ime series employed. Two nonsaionary ime series are co-inegraed if hey move ogeher over ime. We apply he mehod inroduced by Engle and Granger (987 o es for co-inegraion beween he non-saionary ime series. The es involves performing an Augmened Dickey-Fuller es on he residual u of he regression models o deermine if i is saionary as u u (7 ~ The es rejecs or acceps he null hypohesis of no co-inegraion or non-saionariy based on he value of saisic obained in (7. If he residual is saionary (I(0, he ime series are co-inegraed. The ime series ha are no co-inegraed or saionary are correced using differen ransformaions such as differencing and oher mehods. If hese ransformaions fail o induce co-inegraion for Eqs (6, he oupu gap may alernaively be deermined using linear or quadraic models saed in he previous sub-secion. C. Auoregressive Disribued Lags In carrying ou he OLS regressions for he ime series models above, smaller sample sizes may be a cause of concern as he errors or disurbances may be serially correlaed. We adop he mehod of Auoregressive Disribued Lags (henceforh ARDL o deal wih his issue here. An ARDL model reas he auocorrelaion dynamics as par of he model hereby including he lagged dependen variable as well as he lagged independen variable. In general an auoregressive model wih finie disribued lags is called ARDL (p,q which has p lags of dependen variable and q lags of independen variable. The model implies he absence of error auocorrelaion and he number of lags required so as o yield consisen variance esimaors. We esimae he ARDL (, model of equaions (2 and (5 which already consis of forward and backward lagged variables. We consider original uncorreced daa as before, he resuls show ha he variables are fairly more significan in case of (2 as compared o (5. D. Error Correcion Mechanism There may be delays or lags involved in he relaionships esablished in eqs (2, (5 due o which i may ake he sysem longer ime o adjus. In order o deec he presence of a long erm relaionship beween he variables on lef and righ hand side we employ he Error Correcion Mechanism (henceforh ECM. ECM can be applied o any model ha esimaes he rae a which changes in dependen variable come back o equilibrium when here is a change in he independen variable. In 6 ASARC WP 203/06

7 Inflaion, is Volailiy and he Inflaion-Growh Tradeoff in India his model Y * is he desired level of dependen variable Y ha would correspond o he level of independen variable X in he long run Y * 2 X u (8 In he shor run he change in Y depends on he discrepancy beween appropriae and observed values a he previous ime and he change in independen variable. Y * ( Y Y X u (9 Thus ECM jusifies he long run relaion beween dependen and independen variables and he shor run changes in dependen variables in response o long run equilibrium. This is applied in he general model as Y X ( X Y u (20 2 Here δ represens he shor run effec of X on Y and λ is he rae a which he model re-equilibraes. We apply his mehod o our equaions (2, (5. V. RESULTS Time series plos of he key variables used in he analysis for he period are repored in Figures o 4. Figure plos log CPI, figure 2, log of oupu gap, figure 3 inflaion and figure 4 plos inflaion volailiy. There does no appear o be a break in any of he ime series. Figures o 4 here Our esimaion of he wo equaions (2, (5 for India reveals ha he problem of non-saionariy or absence of co-inegraion does no occur for any of he variables. However, in he esimaion of he expeced inflaion volailiy wih eq. 6(d, he series are inegraed of order (i.e., I(. We employ differencing o make hem saionary or I(0. Table presens resuls on OLS esimaion of inflaion volailiy for he period 960 o Oupu gap y has a small negaive bu insignifican effec; Inflaion has a srong negaive significan effec and expeced inflaion has srong posiive significan effec on inflaion volailiy. Table here. Table 2 presens resuls on OLS esimaion of expeced inflaion volailiy using Eq. 5. We find ha he oupu gap drops ou; he level of inflaion has a posiive and highly significan effec; price has a small, posiive and fairly significan effec; expeced price has a small posiive and insignifican effec. ASARC WP 203/06 7

8 Raghbendra Jha & Varsha S. Kulkarni Table 2 here. Table 3 repors resuls on ARDL (, esimaion of Inflaion volailiy. Our principal resuls are as follows: Oupu gap and lagged oupu gap have small negaive and insignifican effecs; Inflaion has a srong negaive and significan effec; lagged inflaion drops ou; expeced inflaion has a srong posiive and significan effec and lagged expeced inflaion drops ou. Lagged inflaion volailiy has a negaive bu insignifican effec. Table 3 here. In Table 4 we repor on esimaion of ARDL(, model for analyzing expeced inflaion volailiy. Lagged oupu gap has negaive significan effec; lagged inflaion has a very small and insignifican effec; price has a posiive and highly significan effec; expeced price has a negaive significan effec. Oupu gap, price, lagged price and lagged expeced price drop ou. Table 4 here. Finally, we repor resuls on ECM esimaion of changes in inflaion volailiy and expeced inflaion volailiy in Tables 5 and 6 respecively. In Table 5 he dependen variable is Change in Inflaion volailiy. Change in oupu gap beween wo successive imes has a small posiive and non significan effec; change in inflaion drops ou; change in expeced inflaion has a srong negaive and highly significan effec; lagged inflaion volailiy has a negaive and highly significan effec; lagged oupu gap has a small negaive bu insignifican effec; lagged inflaion has a negaive and highly significan effec; lagged expeced inflaion has a posiive and significan effec. Tables 5 and 6 here Table 6 models change in expeced inflaion volailiy. None of he variables is significan here. Change in inflaion beween wo successive imes, change in oupu gap, lagged oupu gap and lagged expeced price have almos no effec; change in expeced inflaion has a posiive insignifican effec; lagged expeced inflaion volailiy and lagged expeced inflaion have a small negaive bu insignifican effec; change in expeced price, change in price, lagged inflaion and lagged price drop ou. Hence, as per he ECM esimaion expeced inflaion volailiy appears o be a random process, alhough his is no he case wih he OLS or he ARDL esimaions. VI. DISCUSSION & CONCLUSIONS In his paper we presen resuls on he deerminans of inflaion and expeced inflaion volailiy in he Indian conex. To he bes of our knowledge his is he firs paper o exend he NKPC framework o include inflaion volailiy. 8 ASARC WP 203/06

9 Inflaion, is Volailiy and he Inflaion-Growh Tradeoff in India We employ mehods of OLS and ARDL (, for he esimaion of inflaion and expeced inflaion volailiy as well as changes in hese variables hrough ECM esimaion. OLS esimaion reveals ha acual inflaion volailiy rises wih expeced inflaion and falls when he level of inflaion goes up, alhough he oupu gap has no significan impac. However, in he case of expeced inflaion volailiy he level of inflaion has a srong posiive and significan impac whereas price has a posiive bu only weakly significan impac. Expeced price is insignifican. Since some of he variables used are non-saionary we also repored on ARDL esimaion of he deerminans of inflaion volailiy and expeced inflaion volailiy. In he case of inflaion volailiy oupu gap, lagged oupu gap and lagged inflaion volailiy are all insignifican. The level of inflaion has a negaive significan impac whereas he level of expeced inflaion has a posiive and significan impac. In he case of expeced inflaion volailiy lagged oupu gap has a negaive and significan impac, he price level has a posiive and significan impac whereas expeced price has a negaive and weakly significan impac. Lagged inflaion is insignifican. ECM esimaion reveals change in inflaion variabiliy falls significanly wih lagged inflaion volailiy and lagged inflaion and less significanly wih change in expeced inflaion. I rises wih lagged expeced inflaion alhough he coefficien is only weakly significan. Lagged oupu gap and change in oupu gap are insignifican. The ECM for analyzing change in expeced inflaion volailiy appears o be quie random wih no significan variables. There is evidence ha for some oher counries wih financial liberalizaion here is a reducion in inflaion volailiy and oupu volailiy which is consisen wih heoreical research ha liberalizaion allows risk-sharing, financial markes beer manage raders consumpion decisions, and beer moneary policies bring down oupu volailiy, which in urn may affec inflaion volailiy. Thus our resuls in he Indian conex corroborae he relevance of hese consideraions in he analysis of inflaion volailiy. ASARC WP 203/06 9

10 Raghbendra Jha & Varsha S. Kulkarni REFERENCES Brissimis, S. and N. Magginas (2008, Inflaion Forecass and he New Keynesian Phillips Curve, Inernaional Journal of Cenral Banking, 4(2, 22. Calvo, G. (983, Saggered Prices in a Uiliy-Maximizing Framework, Journal of Moneary Economics, 2 (3, Dornbusch, R., Fischer, S. and Sarz, R (2000 Macroeconomics, 7 h edn, Taa McGraw-Hill, New York and Delhi. Duffy, J. and W. Xiao (20, Invesmen and Moneary Policy: Learning and Deerminacy of Equilibrium, Journal of Money, Credi and Banking, 43(5, Engle, R. and Granger, C (987, Co-inegraion and error correcion represenaion: Esimaion and Tesing, Economerica, 55, Hassler, U. and Wolers, J (2006, Auoregressive disribued lags and co-inegraion, in Saisical Analysis, Springer, 90(, Jha, R. and T. Dang (202, Inflaion Variabiliy and he Relaionship beween Inflaion and Growh, Macroeconomics and Finance in Emerging Marke Economies, 5(, 5 2. Kapur, M. and H. Behera (202, Moneary Transmission Mechanism in India: A Quarerly Model, WPS (DEPR: 09/202, Deparmen of Economic and Policy Research, Mumbai: Reserve Bank of India. Para, D. and P. Ray (200, Inflaion Expecaions and Moneary Policy in India: An Empirical Exploraion, WP/0/84, Washingon DC: The Inernaional Moneary Fund. 0 ASARC WP 203/06

11 Inflaion, is Volailiy and he Inflaion-Growh Tradeoff in India Table : Esimaion of Inflaion Volailiy (Equaion 2 for India (Dependen variable inflaion volailiy Independen Variable Variable Descripion Coefficien -value P> Y Π π e Oupu Gap Level of Inflaion Expeced Inflaion ( ( ( *** *** 0.00 _cons Consan Noes: Daa source: CPI and GDP from IMF daabase for Sandard error in parenhesis. Number of observaions: 46, F(3, 42 = 7. 20, Prob > F = , R-squared =0.3397, Adjused R-squared=0.2925, Roo MSE =.434 Source SS df MS Model Residual Toal Noe Source: CPI, GDP from IMF daabase; p-values * 0. ** 0.0 *** 0.00 **** <0.00; sandard error in parenheses Table 2: Esimaion of Expeced inflaion volailiy (Eq. 5 for India Independen Variable Variable Descripion Coefficien -value P> Π P EP _cons Level of Inflaion Price Expeced price Consan ( ( ( ( *** * ** 0.09 Noes: Daa source: CPI and GDP from IMF daabase for Sandard error in parenhesis. Number of observaions: 46, F(3,42 = 06.4, Prob > F = 0.000, R-squared = , Adjused R-Squared = , Roo MSE = Source SS df MS Model Residual Toal Noe Source: CPI, GDP from IMF daabase; p-values * 0.5** 0. *** **** <0.003; sandard error in parenheses ASARC WP 203/06

12 Raghbendra Jha & Varsha S. Kulkarni Table 3: Resuls of ARDL (, model for analyzing inflaion volailiy (Eq.2 for India Variable Name Variable Descripion Coefficien -score P > Y Ly Π π e Led π e _cons Oupu Gap Lagged oupu gap Inflaion Expeced inflaion Lagged inflaion volailiy Cons ( ( ( ( ( ( ** ** Number of observaions: 45, F(5,39=4.24, Prob>F=0.0036, R-squared=0.3523, Adjused R-squared= , Roo MSE =.75. Source SS Df MS Model Residual Toal Noe Source: CPI, GDP from IMF daabase; p-values * <0. ** 0.05 *** 0.00 **** <0.00; sandard error in parenheses Table 4: Resuls of ARDL (, model for analyzing expeced inflaion variabiliy (Eq.5 for India Variable Name Variable Descripion Coefficien -score P > L y L π P ep _cons Lagged oupu gap Lagged inflaion Price Expeced Price Consan ( ( ( ( ( ** *** * ** Number of observaions: 45, F(4,40=86.47, Prob>F=0.000, R-squared=0.8963, Adjused R-squared= , Roo MSE = Source SS df MS Model Residual Toal Noe Source: CPI, GDP from IMF daabase; p-values * 0. ** 0.07 *** 0.03 **** <0.00; sandard error in parenheses 2 ASARC WP 203/06

13 Inflaion, is Volailiy and he Inflaion-Growh Tradeoff in India Table 5: Resuls of ECM for analyzing change in inflaion volailiy (Eq.2 for India Variable Name Variable Descripion Coefficien -score P > Dy dπ e Ly Led π e Lπ Lπ e _cons Change in oupu gap Change in expeced inflaion Lagged Oupu Gap Lagged inflaion volailiy Lagged inflaion Lagged Expeced inflaion Consan ( ( ( ( ( ( ( * *** ** * * Number of observaions = 45, F(6,38 =22.0, Prob>F=0.0000, R-squared=0.778, Adj R-squared = , Roo MSE =.456. Source S f MS Model Residual Toal Noe Source: CPI, GDP from IMF daabase; p-values * <0. ** 0.04 *** 0.00 **** <0.00; sandard error in parenheses Table 6: Resuls of ECM for analyzing change in expeced inflaion volailiy (Eq.5 for India Variable Name Variable Descripion Coefficien -score P > Dπ Dπ e Dy L dπ e L π e LeP Ly _cons Change in inflaion Change in expeced inflaion Change in oupu gap Lagged expeced inflaion volailiy Lagged expeced inflaion Lagged Expeced price Lagged oupu gap Consan ( ( ( ( ( ( ( ( Number of observaions = 45, F(7,37 =0.37, Prob>F=0.935, R-squared=0.065, Adj R-squared = -0., Roo MSE = Source SS df MS Model Residual Toal Noe Source: CPI, GDP from IMF daabase; p-values * 0.6 ** 0.0 *** **** <0.00; sandard error in parenheses ASARC WP 203/06 3

14 Raghbendra Jha & Varsha S. Kulkarni 5 Log CPI ime series for India Log(price Time(years Figure 3 Log Oupu gap ime series 2 Log(Oupu gap Time(years Figure 2 4 ASARC WP 203/06

15 Inflaion, is Volailiy and he Inflaion-Growh Tradeoff in India 9 Inflaion ime series for India Inflaion Time(years Figure 3 6 Inflaion volailiy ime series for India 4 Inflaion Volailiy Time(years Figure 4 ASARC WP 203/06 5